116 
.MK. B. D. STEELE OX THE MEASUEE.MEXT OF IONIC VELOCITIES 
be seen, and a superior limit above which the Ijoundary is rendered useless for obser¬ 
vation by the “washing” and “mixing” effect of too great a current density and 
consequent heating. For a few pairs of solution it has not been found possible to 
obtain a refraction margin under any conditions that have been tried. 
The potential fall in all cases is calculated on the assumption that the solution 
l^etween the two boundaries is homogeneous, being of the same concentration and 
specific resistance throughout. Since Ohm’s Law holds good for electrolytes, E = CR ; 
and from the specific resistance r the resistance of 1 centim. of the liquid column 
is obtained by dividing by the area of the tube, and hence the potential fall 
c/tt C r 
dx A 
section of the column of liquid. 
A striking example of the influence of 23 otential fall on the condition of the 
maigin is seen in the case of a normal solution of barium chloride, using the apparatus 
shown in fig. i. With magnesium chloride and sodium acetate as indicators the 
anion boundary is that between barium acetate and barium chloride, and will be 
uA.c 
rejDresented by Ba , the cation boundary that between magnesium chloride and 
barium chloride = ~ CT. Starting the experiment with a potential fall of 1 volt per 
centim., a fair but not very good anion boundary is produced, but there is no sign of 
a boundary at the other end ; on increasing the voltage to 1 ‘ 20 , the anion margin 
becomes very sharp and easy to read. At the cation end the gas flame, when viewed 
through the telescope of the cathetometer, is seen to be slightly distorted, but no 
boundary has yet appeared. With a voltage of IA the anion boundary shows signs 
of “ washing,” whilst that at the cation end is still too indistinct for use. At 
2'0 volts it has become good and distinct, whilst from the anion margin little 
whirlpools are seen to rise, and it has become undulating and sharp as though it were 
cut with a knife. With further increased potential fall the cation boundary remains 
good, until about 3’5 volts, when it, in its turn, begins to show signs of “washing” 
and consequent mixing. 
Y V 
For the determination of the ratio — or ^ ^ for salts which, like barium chloride, 
require a different potential fall at the two boundaries, the form of apparatus shown 
in fig. 3 has been found suitable. 
Here the tubes to be used for the measurement are four in number, and are 
indicated by the letters A, B, and C. The sectional areas of these tubes are different, 
and each is carefully calibrated, and its area of cross-section determined. Since the 
potential fall— ^ , it follows that, by selecting tubes of different sizes, any 
required ratio between the potential falls at the two margins may be easily obtained. 
It is found in practice that three sizes of tubes are sufficient for all the cases that are 
, where C is the current, r the specific resistance, and A the area of cross- 
